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A030171 Decimal expansion of real number y such that y = Gamma(x) is a minimum.

%I A030171 #52 Feb 16 2025 08:32:35
%S A030171 8,8,5,6,0,3,1,9,4,4,1,0,8,8,8,7,0,0,2,7,8,8,1,5,9,0,0,5,8,2,5,8,8,7,
%T A030171 3,3,2,0,7,9,5,1,5,3,3,6,6,9,9,0,3,4,4,8,8,7,1,2,0,0,1,6,5,8,7,5,1,3,
%U A030171 6,2,2,7,4,1,7,3,9,6,3,4,6,6,6,4,7,9,8,2,8,0,2,1,4,2,0,3,5,9
%N A030171 Decimal expansion of real number y such that y = Gamma(x) is a minimum.
%D A030171 Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 34.
%H A030171 G. C. Greubel, <a href="/A030171/b030171.txt">Table of n, a(n) for n = 0..5000</a>
%H A030171 Simon Plouffe, <a href="http://www.plouffe.fr/simon/constants/minygam.txt">Minimal point of GAMMA(x)</a>.
%H A030171 Simon Plouffe, <a href="http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap68.html">Minimal y of GAMMA(x)</a>.
%H A030171 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GammaFunction.html">Gamma Function</a>.
%e A030171 0.885603194410888700278815900582588733207951533669903448871200165875136...
%p A030171 Digits:=500; x0:=fsolve(Psi(x)=0, x); evalf(GAMMA(x0), 120) # _Iaroslav V. Blagouchine_, Feb 16 2016
%t A030171 First@ RealDigits[ FindMinimum[ Gamma[x], {x, 1.4}, WorkingPrecision -> 2^7][[1]]] (* _Robert G. Wilson v_, Aug 03 2010 *)
%t A030171 RealDigits[ Gamma[x /. FindRoot[ PolyGamma[0, x] == 0, {x, 1}, WorkingPrecision -> 100]]][[1]] (* _Jean-François Alcover_, Oct 23 2012 *)
%o A030171 (PARI) gamma(solve(x=1,2,psi(x))) \\ _Charles R Greathouse IV_, Apr 17 2015
%Y A030171 Cf. A030169 for value of x.
%K A030171 nonn,cons
%O A030171 0,1
%A A030171 _Eric W. Weisstein_